Methods and apparatus for regulating transmembrane ion movement utilizing selective harmonic frequencies and simultaneous multiple ion regulation

ABSTRACT

Methods and apparatus for regulating ion movement across biological membranes are provided. In one aspect, harmonic frequencies of a fluctuating magnetic field based on cyclotron resonance principles are provided for selectively enhancing transmembrane ion movement. In another aspect, a method and apparatus are provided for simultaneously regulating the transmembrane movement of multiple distinct ionic species using a fluctuating magnetic field. Therapeutic applications of harmonic tuning and multiple tuning are also provided.

INTRODUCTION

This patent application is a continuation in part of each of thefollowing U.S. patent applications, the disclosures of which are allexpressly incorporated herein by reference: U.S. patent application Ser.No. 280,848, filed Dec. 7, 1988, which is a continuation of U.S. patentapplication Ser. No. 923,760, filed Oct. 27, 1986, entitled "TechniquesFor Enhancing the Permeability of Ions Through Membranes," now U.S. Pat.No. 4,818,697; U.S. patent application Ser. No. 172,268, filed Mar. 23,1988, entitled "Method and Apparatus for Controlling Tissue Growth Withan Applied Fluctuating Magnetic Field", U.S. Pat. No. 4,932,951 ; U.S.patent application Ser. No. 265,265, filed Oct. 31, 1988, entitled"Method and Apparatus for Controlling the Growth of Cartilage", U.S.Pat. No. 5,067,940; U.S. patent application Ser. No. 254,438 filed Oct.6, 1988, entitled "Method and Apparatus for Controlling the Growth ofNon-Osseous, Non-Cartilaginous Solid Connective Tissue"; and U.S. patentapplication Ser. No. 295,164, filed Jan. 9. 1989, entitled "Techniquesfor Controlling Osteoporosis Using Non-Invasive Magnetic Fields," all ofwhich have been assigned to the assignor of the present invention.

FIELD OF THE INVENTION

The present invention relates generally to methods and apparatus forregulating the movement of ions across cell membranes. Morespecifically, the present invention provides methods and apparatus forregulating the transmembrane movement of preselected ions in biologicalsystems using selected harmonic frequencies which are based on thecharge-to-mass ratio of the preselected ions. The present invention alsoprovides a method and apparatus for simultaneously regulating thetransmembrane movement of two or more distinct ionic species across amembrane. The present invention further provides methods and apparatusfor the therapeutic treatment of selected body tissues.

BACKGROUND OF THE INVENTION

The role of biological ions as mediators of cellular activity is wellestablished. In U.S. patent application Ser. No. 923,760, the inventorsof the present invention disclose novel techniques for controlling themovement of a preselected ionic species across the membrane of a livingcell. Therein, the relationship between ion movement and fluctuatingmagnetic fields is described and a method and apparatus are provided bywhich ion movement can be selectively controlled. Having discovered thation movement through a biochemical membrane can be controlled bycreating a specific relationship between the strength of a fluctuatingmagnetic field and the rate of the field oscillation, and that therelationship can be predicted using the cyclotron resonance equation,the frequency of which is: ##EQU1## the present inventors provided afoundation on which a number of useful inventions are based.

Accordingly, in U.S. patent application Ser. No. 923,760, it isdisclosed that by exposing a region of living tissue of a subject suchas a human or animal subject to an oscillating magnetic field ofpredetermined flux density and frequency, the rate of tissue growth canbe controlled. Specifically, it is disclosed therein that by tuning afluctuating magnetic field to the specific cyclotron resonance frequencyof a preselected ion such as Ca⁺⁺ or Mg⁺⁺, the rate of bone growth canbe stimulated. It is anticipated that this treatment will be highlybeneficial in the treatment of fractures, bone non-unions, and delayedunions. In addition, the use of cyclotron resonance tuning to controlthe growth rate of non-osseous, non-cartilaginous connective solidtissue is described in U.S. patent application Ser. No. 254,438. In U.S.patent application Ser. No. 265,265, a method and apparatus based oncyclotron resonance tuning are disclosed which allow the growth rate ofcartilaginous tissue to be regulated. Still another important use ofcyclotron resonance tuning, one of particular significance in thetreatment of elderly patients, is disclosed in U.S. patent applicationSer. No. 295,164. Therein, a method and apparatus for treating andpreventing osteoporosis, both locally and systemically, is set forth.Therefore, it will be appreciated that cyclotron resonance regulation ofion movement is instrumental in a number of highly beneficial inventionsin the field of medicine.

As described more fully in the foregoing United States patentapplications, the inventors of the present invention discovered that ionmovement through cell membranes can be achieved with the use of amagnetic field generating device in connection with an oscillator forcreating a fluctuating magnetic flux density where a predeterminedrelationship between frequency and field strength is established.Preferably the magnetic field generating device includes a pair ofHelmholtz coils. A cell or region of tissue, such as bone, cartilage orthe like, is positioned between the Helmholtz coils such that a uniformmagnetic field of controlled parameters permeates the target cell ortissue. As will be appreciated, in most instances the cell or tissuewhich is exposed to the applied magnetic field is also subject to alocal magnetic field having a component in the direction of the appliedfield. In these applications, a magnetic field sensing device isprovided to measure the combined or total magnetic flux, i.e. the sum ofthe applied magnetic field parallel to an axis which extends through thecell and the component of the local field in this direction.

In the preferred embodiments of the foregoing inventions, thecharge-to-mass ratio of an ion, the transmembrane movement of which isto be regulated, is used to determine the frequency at which the appliedmagnetic field is oscillated to provide a predetermined relationshipbetween the charge-to-mass ratio of the ion and the strength andfrequency of the magnetic field. This relationship is determined usingthe cyclotron resonance equation, f_(c) =Bq/2πm, where f_(c) is thefrequency of the oscillating magnetic field in Hertz, q/m is thecharge-to-mass ratio of the ion in Coulcombs per kilograms, and B is anon-zero average value of the magnetic flux density in Tesla along theaxis permeating the subject cell or tissue. When the field includes acomponent of the local field, this value is a non-zero net average valueof the combined or resultant magnetic field.

The present invention is directed toward certain modifications incyclotron resonance regulation of ion movement. More specifically, thepresent invention addresses the desirable goal of simultaneouslyregulating transmembrane movement of two different ionic species, forexample Ca⁺⁺ and Mg⁺⁺, and also to additional frequencies which areeffective for a single ion.

Therefore, it is an object of the present invention to provide a methodand apparatus by which the movement of a single ionic species across acell membrane can be regulated by a fluctuating magnetic field having afrequency selected from a group of frequencies based on the fundamentalcyclotron resonance frequency. It is a further object of the presentinvention to provide a method and apparatus by which the transmembranemovement of two or more distinct ionic species in a single system may besimultaneously regulated using a fluctuating magnetic field having apredetermined ratio between the frequency and average field strength. Itis still a further object of the present invention to provide a numberof techniques for the therapeutic treatment of biological subjects whichare based on the tuning principles set forth herein.

SUMMARY OF THE INVENTION

In accordance with the present invention there is provided in one aspecta method for regulating the movement of a preselected ion across a cellmembrane. The method includes the steps of generating an appliedmagnetic field parallel to a predetermined axis which projects through aspace in which at least one living cell or a target tissue ispositioned. The cell or target tissue is surrounded by a fluid in thepresence of a preselected ion. The applied magnetic field, alone or incombination with a component of the local magnetic field parallel to thepredetermined axis, permeates the target cell or tissue. The appliedmagnetic field is fluctuated at a predetermined rate such that themagnetic flux density along the predetermined axis, which in thepresence of a local magnetic field includes the local component, has anon-zero average value.

Transmembrane movement of a preselected ion is controlled by creatingand maintaining a predetermined relationship between the frequency ofthe fluctuations and the non-zero average value of the magnetic fluxdensity along the predetermined axis based on the charge-to-mass ratioof the preselected ion. This predetermined relationship is determinedusing the equation f_(ch) =XBq/2πm where f_(ch) is the frequency of thefluctuating magnetic flux density in Hertz, B is the non-zero averagevalue of the flux density parallel to the predetermined axis in Tesla, qis the charge of the preselected ion in Coulombs, m is the mass of thepreselected ion in kilograms, and X is a preselected odd integer greaterthan one. In this manner, a number of higher harmonic frequencies areprovided by which transmembrane movement of a preselected ionic speciescan be regulated. An inventive apparatus for carrying out the method ofthe present invention is also provided.

In another aspect, the present invention provides a method forsimultaneously regulating the transmembrane movement of two or moredifferent ions across a cell membrane. In a preferred embodiment, themethod comprises generating an applied magnetic field parallel to apredetermined axis which projects through a designated space. In thepresence of at least two different predetermined ionic species, a livingcell or tissue in a biological fluid is placed in the designated spacesuch that the target cell or tissue is exposed to the applied magneticfield. In one embodiment, the target cell or tissue is also exposed to alocal magnetic field having a component parallel to the predeterminedaxis. The magnetic flux density along the predetermined axis isfluctuated to create a non-zero average value. Where a local field isalso present, this non-zero average value is the net non-zero averagevalue of the applied and local field components parallel to thepredetermined axis.

A predetermined relationship between the frequency of the fluctuationsand the non-zero average value of the magnetic flux density along theaxis is then created and maintained which simultaneously controls themovement of two or more preselected ions. In one embodiment, thepredetermined relationship is determined by first solving the equationf_(c) =Bq/2πm at a generally randomly selected value of B for eachdistinct preselected ion, where f_(c) is the frequency of the fieldfluctuations in Hertz, B is the non-zero average value of the fluxdensity parallel to the predetermined axis in Tesla, q is the charge ofeach preselected ion in Coulombs, and m is the mass of each preselectedion in kilograms. The value of B is preferably between about 1.0 andabout 10,000 μ Tesla. This establishes the fundamental cyclotronfrequency for each ion. A value f_(cs), not necessarily equal to tof_(c), is then determined at which the magnetic flux density isoscillated. The value of f_(cs) is preferably selected such that none ofthe individual ion f_(c) values deviate more than 5 percent from thef_(cs) value. In most instances, there will be no f_(cs) value availablebased on the fundamental f_(c) values of the preselected ions.Accordingly, a higher odd harmonic frequency of at least one of thepreselected ions is determined with the equation f_(ch) =XBq/2πm aspreviously explained. The values of f_(c) and f_(ch) are examined todetermine whether an f_(ch) value can be selected based on a 10 percentand most preferably a 5 percent deviation factor. If not, the process iscontinued for each value of f_(ch), beginning with the lowest oddharmonic f_(ch) values until a value of f_(cs) can be established withinthe 5 percent deviation. Hence, at the value selected for B during thecalculation of the f_(c) or f_(ch) values, the magnetic flux density towhich the target cell or tissues exposed is fluctuated along the axis atthe f_(cs) frequency. This specific relationship between frequency andfield strength brings about simultaneous transmembrane movement of thepreselected ions. An apparatus adapted to simultaneously regulate morethan one ionic species in this manner is also provided.

In still another aspect of the present invention, the concepts ofharmonic tuning and multiple ion tuning are used for therapeutictreatment of a region of tissue in a human or animal subject. Inparticular, the present invention provides a therapeutic treatmentmodality for bone tissue to stimulate bone growth and/or reduceosteoporosis. In still another embodiment, the growth characteristics ofcartilaginous tissue or non-osseous, non-cartilaginous connective tissueare regulated. In still another aspect, systemic treatment and/orprevention of osteoporosis is also provided.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other advantages and features of the invention will bedescribed more fully hereinafter and in connection with the accompanyingdrawings in which:

FIG. 1 is a schematic, perspective view of a living cell exposed to afluctuating magnetic field in accordance with the present invention.

FIG. 2 is a schematic diagram illustrating the formation of a combinedor net magnetic flux density which includes a local field component inaccordance with the present invention.

FIG. 3 is a schematic electrical diagram of an apparatus for generatingthe ion-regulating, fluctuating magnetic field of the present invention.

FIGS. 4 through 7 illustrate signal waveshapes generated by theapparatus shown in FIG. 3.

FIG. 8 illustrates the present invention for use in local treatment ofliving tissue in vivo.

FIG. 9 illustrates the use of the present invention for providingsystemic therapeutic treatment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring no to FIG. 1 of the drawings, a pair of field coils 10A and10B having the arrangement and attributes set forth more fully in theaforementioned U.S. patent application Ser. No. 923,760 are seen bywhich an applied magnetic field is generated which permeates living cell12 in predetermined volume or space 14. As will become more apparenthereinafter, living cell 12 may comprise one or more distinct cells,cell aggregates, organoids or tissue. In particular, living cell 12 maycomprise a region of tissue such as a region of bone in a living host,either man or animal. Cell 12 contains a specific complement ofintracellular ionic species and will generally be surrounded by a liquidcontaining ionic species required for cell and tissue function.

Coils 10A and 10B, as well as space 14 are shown in relation to arectangular coordinate axis system with the mid-planes of each coilpositioned at X₁, Y₁, and X₂, Y₂ and separated by a distance R. Thecenter of each coil is aligned with the Z-axis and has a radius R'.Those skilled in the art will recognize that coils 10A and 10B arearranged in Helmholtz configuration. Accordingly, a uniform appliedmagnetic field having a flux density B is generated in space 14 by coils10A and 10B. As will be explained more fully, in most applications, Bwill be the average value of the net or combined magnetic flux densityin space 14 resulting from the applied field and a pre-existing localfield component such as the earth's geomagnetic field. Thus, a magneticfield of known, controllable parameters permeates cell 12 along apredetermined axis. The value of B may be preferably measured by amagnetic field sensor or the like. In the present invention, the appliedmagnetic field is fluctuated at a predetermined frequency. Thischaracteristic is illustrated by opposed arrows A1 and A2 which areseparated by a dot "D."

Referring now to FIG. 2 of the drawings, in that embodiment of thepresent invention in which space 14 is subject to a local magneticfield, the local magnetic field will have a component vector in thedirection of the Z-axis which penetrates space 14 and cell 12. TheZ-axis represents the aforementioned predetermined axis which extendsthrough the target cell or tissue to be influenced in accordance withthe present invention. It is that component of the magnetic fieldparallel to this predetermined axis which is regulated to producetransmembrane ion movement in the present invention. In FIG. 2, theapplied magnetic field which is parallel to the predetermined axis Z isshown as B_(o). The local magnetic field component parallel to theZ-axis is illustrated as B_(z). It is to be understood that space 14represents the region in which the magnetic flux density as regulated bythe present invention is substantially uniform. Space 14 should be largeenough to accommodate the target cell or tissue to be treated. In thisembodiment, B is the average value of the combined applied and localfield components, i.e. the net average value of the sum of B₀ and B_(Z).

Referring now to FIG. 3 of the drawings, in one embodiment coils 10A and10B receive electrical signals from a conventional AC sine wavegenerator 16 connected by means of a switch 18 either to a DC offsettingnetwork 20 or a full-wave rectifier 22, although other waveforms may besuitable. The instantaneous current I supplied to coils 10A and 10B as afunction of time is shown for both switch positions 18A and 18B in FIGS.4 and 5, respectively. Similarly, the instantaneous magnetic fluxdensity, B_(o) in FIG. 2, produced within space 14 is depicted as afunction of time for both switch positions 18A and 18B in FIGS. 6 and 7,respectively.

When coils 10A and 10B are energized by the apparatus shown in FIG. 3 ofthe drawings, the coils generates a magnetic flux density within volume14 that varies with time as shown in FIGS. 6 and 7. An applied non-zeroaverage magnetic flux density B, uniform throughout spacer 14, resultseither from an offset sinusoidal signal or from a full-wave rectifiedsignal applied to coils 10A and 10B. As stated, where space 14 issubject to a local magnetic field, B is the net non-zero averagemagnetic flux density of the applied and local field parallel to thepredetermined axis. The effect of this Z-component of the local fluxdensity will be to change the non-zero average applied magnetic fluxdensity B_(o) shown in FIG. 2 to a different net average value.

As fully explained in the aforementioned U.S. patent application Ser.No. 923,760, be creating a relationship between the rate of fluctuationor frequency of the magnetic field parallel to the predetermined axiswhich extends through space 14 and thus through the target tissue orcell 12, and the magnetic flux density along this axis, a fundamentalfrequency based on the charge-to-mass ratio of a preselected ionicspecies can be determined at which movement of the preselected ionicspecies across the cell membrane can be regulated. The parameters ofthis relationship are determined with reference to the cyclotronresonance frequency f_(c) =Bq/2πm. In other words, the magnetic fluxdensity along the Z-axis, which includes a local component vector if alocal field exists, is regulated such that the charge-to-mass ratio ofthe preselected ion equals the ratio of 2π times the supplied frequencyf_(c) times the non-zero average magnetic flux density B.

In the present invention, this fundamental frequency, f_(c), iseffectively multiplied by a selected odd integer to produce a frequencywhich also causes the preselected ion to move across the cell membraneof cell 12. Unless otherwise specified, as used herein, the term "oddintegers" or "odd integer" shall mean positive, non-zero integers. Thepreferred odd integers for use in the present invention which provideharmonic frequencies that are effective in causing transmembrane ionmovement are selected from the group consisting of the followingintegers: three, five, seven, nine, eleven, thirteen, fifteen, seventeenand nineteen. Additional harmonic frequencies based on multiplying thefundamental frequency by an odd integer may also be suitable in someapplications. Even integers have not been found useful. The frequenciesfor a given preselected ion and known magnetic flux density B can bedetermined with reference to the equation f_(ch) =XBq/2πm where f_(ch)is the frequency in Hertz of the fluctuating magnetic field along apredetermined axis extending through the target tissue, B is themagnetic flux density along the axis in Tesla, q is the charge of thepreselected ion in Coulombs, m is the mass of the preselected ion inkilograms, and X is a selected odd integer greater than one. It has beenfound that many of the preferred odd multiple harmonic frequencies aresubstantially as effective in promoting transmembrane ion movement asare the fundamental frequencies. As stated, the preferred values of Xare the odd integers three, five, seven, nine, eleven, thirteen,fifteen, seventeen, and nineteen. Ion movement of a number of ionicspecies can be controlled or regulated in this manner, including Ca⁺⁺,Mg⁺⁺, K⁺, Li⁺, Na⁺, Cl⁻ and HCO₃ ⁻. Other ions may be also suitable in aparticular application.

In those applications where random changes in the local field componentalong the predetermined axis may occur, it is preferred that themagnetic field generating device of the present invention include amagnetic field sensor, such as a Hall effect device, to measure themagnetic flux density B along the predetermined axis. It is alsopreferred that microprocessing means described in the aforementionedU.S. patent application Ser. No. 172,268 be included with the fieldgenerator and magnetic sensor such that the rate of fluctuation (f_(ch))of the field and/or the value B of the field can be automaticallychanged to compensate for changes in the local field component. Thisallows the predetermined relationship to be maintained despite theselocal changes.

In the preferred embodiment of the present invention, the concept oftuning the cyclotron resonance frequency to an odd harmonic aspreviously described is used in connection with the therapeutictreatment modalities as described in the aforementioned U.S. patentapplications Ser. Nos. 172,268, 265,265, 254,438 and 295,164. Morespecifically, and referring now to FIG. 8 of the drawings, treatmentapparatus 30 is shown having treatment heads 32 and 34, each of whichencloses a field coil such that treatment heads 32 and 34 comprise apair of Helmholtz coils by which a uniform magnetic field is generatedin space 36, which in this instance is occupied by a region of livingtissue. The general design of treatment apparatus 30 is explained inmore detail in U.S. patent application Ser. No. 172,268, which isincorporated herein by reference. Accordingly, and for the purposes ofillustration, a human femur 38 having fractured ends 40 and 42 is shownin phantom within leg 44. In order to stimulate the growth of fracturedends 40 and 42, a fluctuating magnetic field is established usingtreatment apparatus 30 in which the frequency of fluctuations isdetermined with reference to the aforementioned modification of thecyclotron resonance equation: f_(c) =XBq/2 πm. In a preferred aspect, Xis 3 and the preselected ionic species is calcium. Magnesium andpotassium regulation, in addition to other ions, is also useful.Accordingly, in one preferred embodiment, a frequency of 15.31 Hertz isestablished for the Ca⁺⁺ ion where the combined or composite magneticflux density parallel to a predetermined axis A has a net non-zeroaverage value of 20.0μ Tesla and a peak-to-peak amplitude of 40.0μ Teslato stimulate bone growth. The higher harmonic tuning of the presentinvention is similarly useful in the regulation of cartilage growth andthe growth of non-osseous, non-cartilaginous connective tissue asdescribed in the aforementioned U.S. patent applications. Forstimulating cartilage growth a frequency of 75.71 Hertz at a B value of20.0μ Tesla with a peak-to-peak amplitude of 40.0μ Tesla is suitable.This represents cyclotron resonance tuning for the Mg⁺⁺ ion where X is3. In the case of non-cartilaginous, non-osseous solid connective tissuea frequency of 15.31 Hertz with a B value of 20.0 μ Tesla andpeak-to-peak amplitude of 40.0μ Tesla is suitable for stimulatinggrowth. This represents cyclotron resonance tuning to the Ca⁺⁺ ion whereX is 1.

The present invention is also useful in the systemic treatment and/orprevention of osteoporosis as will now be described in connection withFIG. 9 of the drawings. Accordingly, systemic treatment apparatus 50 isshown which comprises a tube or cylinder 52 of a non-magnetic materialsuch as plastic. Tube 52 houses a large solenoid 54 which containsmultiple turns of wire 56 which extend substantially the entire lengthof systemic treatment apparatus 50. A gurney or platform 58 is providedon a track system (not shown) which allows platform 58 to move between afirst position outside tube 52 to a second position inside tube 52. Acontroller 60 is provided along with the necessary circuitry forenergizing solenoid 54 to create a magnetic field in the direction ofaxis 62, which in this embodiment projects through the central bore ofsolenoid 54 and subject 59. A fluctuating, and in most instances acombined or composite magnetic field, having a magnetic flux densityparallel to predetermined axis 62 is generated. The combined magneticflux density along the axis is maintained at a predeterminedrelationship to the frequency of the fluctuations. Again, the frequencyof the fluctuating field is determined with reference to the equationf_(c) =XBq/2πm, where X is a selected odd integer. In the most preferredembodiment, the preselected ionic species to which the fluctuatingmagnetic field is tuned using this odd harmonic technique comprises Ca⁺⁺where X is 5. This treatment is effective in diminishing or preventingosteoporosis in a human or animal subject.

In still another aspect of the present invention, a method and apparatusfor simultaneously regulating the transmembrane movement of twodifferent ionic species is provided. This technique is based in part onthe principles of odd harmonic frequencies as described above. In thedevelopment of cyclotron resonance tuning, the present inventorsrecognized that it may be desirable in some instances to simultaneouslyregulate the transmembrane movement of two or more preselected ions. Inthis manner, the benefits of ion movement of each such ion could beachieved simultaneously, and quite possibly, a beneficial synergismmight be achieved. One such method of simultaneous multiple ionregulation is set forth in the aforementioned U.S. patent applicationSer. No. 923,760. Therein, a method is disclosed for simultaneouslyenhancing the transmembrane movement of two distinctly different ionicspecies such as a hydrogen ion and a potassium ion. In the presentinvention, multiple ion tuning is achieved by regulating magnetic fluxdensity along a single axis. In accordance with the present invention, arelationship between the frequency of the fluctuating magnetic field anda non-zero average value of the magnetic flux density is provided suchthat the field is simultaneously tuned to effect transmembrane movementof more than one type of ionic species at the same time.

More specifically, it has been found that the fundamental cyclotronresonance frequency of a preselected ionic species may be within a fewpercent of a selected odd multiple of the fundamental frequency of adifferent ionic species. In addition, an odd harmonic cyclotronresonance frequency of one preselected ionic species may besubstantially the same as a different odd harmonic frequency of anotherpreselected ionic species. This principle of "harmonic overlap" may beextended to three, four, or possibly even a greater number of differentionic species where a "common" frequency can be found which issubstantially equal to a fundamental or odd multiple harmonic frequencyof each of the ionic species involved. In this manner, it is possible tosimultaneously regulate the transmembrane movement of two or moredifferent ionic species.

With reference now again to FIG. 1 of the drawings, the target tissue orcell 12 is placed between coils 10A and 10B in space 14, again in thepresence of a liquid medium which may be the natural cell environment.At least two different ionic species to be regulated are present. Amagnetic field having a flux density along a predetermined axis, the Zaxis in FIG. 1, is generated in most embodiments a local magnetic fieldhaving a component along the predetermined axis will be present. Anon-zero average value or net average value of the magnetic flux densityto be initiated parallel to the axis is then selected. The value of B ispreferably between about 1.0 to about 10,000μ Tesla, with a peak-to-peakamplitude of about 2.0 to about 20,000μ Tesla.

In one embodiment the fundamental frequency at which the fluctuatingmagnetic field would be oscillated for cyclotron resonance regulation oftransmembrane ion movement is calculated individually for each differentionic species to be regulated using the equation f_(c) =Bq/2πm for aselected value of B, which is again the non-zero average value of theflux density along the predetermined axis. As previously explained,f_(c) as in Hertz, q as in Coulombs, and m is in kilograms. q/m is thecharge-to-mass ratio of the preselected ion. Once the fundamentalcyclotron resonance frequency (f_(c)) of each ion to be regulated iscalculated, a regulating frequency (f_(cs)) is determined which ispreferably within 5 percent of the fundamental frequency f_(c) or an oddharmonic frequency f_(ch) of each preselected ion. The odd harmonicfrequencies are determined again using the equation f_(ch) =XBq/2πm,where X is an odd integer greater than one. It will be understood thatthe equation f_(ch) =XBq/2πm can be used to determine the fundamentalfrequency, f_(c), by using a value of 1 for X. While the value of f_(cs)will not typically be available which is common to the fundamentalfrequencies and/or odd harmonic frequencies for each preselected ion, ithas been found that an f_(cs) value which is within about 10 percent andpreferably about 5 percent of each fc value or f_(ch) value of the ionsto be regulated satisfactorily provides simultaneous transmembranemovement of each preselected ion in the field.

It will also be understood that the values of f_(ch) are a function ofB. Thus, it may be possible to obtain an f_(cs) value for a particularset of ions which is within the preferred 5 percent deviation at adesignated B value, but not a higher B value. For use in the presentinvention as applied to multiple simultaneous ion tuning, the value of Bis preferably between about 1.0 to about 10,000μ Tesla, with apeak-to-peak amplitude of about 2.0 to about 20,000μ Tesla. Again, thewaveform is not critical.

Accordingly, and referring now to FIG. 1 of the drawings, a magneticflux density is generated with coils 10A and 10B along the Z axis whichfluctuates at the multiple harmonic tuning value f_(cs). The sameconsiderations applicable in the previous embodiments with respect tothe local component are also applicable to multiple ion tuning.

In order to fully illustrate this embodiment of the present invention,multiple ion tuning will be described in the case of two preferred ions,Ca⁺⁺ and Mg⁺⁺. Referring to Table 1 below,

                  TABLE 1                                                         ______________________________________                                        ION      q/m RATIO  X 3       X 5   X 15                                      ______________________________________                                        Ca.sup.++                                                                              76.563     229.689   382.815                                                                             1148.445                                  Mg.sup.++                                                                              126.178    378.534   630.89                                                                              1892.67                                   ______________________________________                                    

the q/m ratios for Ca⁺⁺ and for Mg⁺⁺ are set forth along with the valuesof certain multiples of the q/m ratio, specifically 3, 5 and 15. It willbe recognized that f_(ch) is a function of the q/m ratio of each ion.For the Mg⁺⁺ ion 3q/m is within 1.2% of the value of 5q/m for thecalcium ion. Thus, for a given value of B, for example, 20 microTesla,where X is 3 for Mg⁺⁺ and X is 5 for Ca⁺⁺, a range of values f_(cs) canbe determined which are within 5 percent of each f_(ch) value. Morespecifically, in this example f_(ch) for Mg⁺⁺ at 20 microTesla where Xis 3 75.71 Hertz. Where X is 5, f_(ch) for Ca⁺⁺ is 76.56 Hertz. It willbe recognized that a number of values f_(cs) can be selected which arewithin 5 percent of both f_(ch) values. In one preferred embodiment, themean value for the two f_(ch) values is determined for use as the f_(cs)value which is this example is 76.14 Hertz. An f_(ch) value whichdeviates more than 5 percent from one or all of the f_(c) or f_(ch)values for the various ions may be suitable in some applications,although this 5 percent standard is preferred.

In another aspect, the multiple ion tuning of the present invention canbe described in the case of harmonic overlap of two preselected ions inthe following manner. A normalized cyclotron resonance frequency (f_(c)/B₀) is calculated using the equation: ##EQU2## where B₀ is the magneticflux density in Gauss along the axis, N is the valence charge number ofthe preselected ion (for example, N=2 for the Ca⁺⁺ ion and N=1 for the(Cl⁻ ion); q is 1.6×10⁻¹⁹ Coulombs; and m is the ionic mass of thepreselected ion in kilograms. Since it is known that ##EQU3## Byspecifying a value for B₀, equation III above provides the fundamentalcyclotron resonance frequency for the preselected ion. To then determineharmonic overlaps for two preselected ions, the following equation maybe utilized: ##EQU4## where (f_(c) /B₀)_(j) is the normalized cyclotronresonance frequency for a preselected ion "j"; (fc/B₀)_(k) is thenormalized cyclotron resonance frequency for a preselected ion "k";H_(j) is the harmonic number for ion "j"; and H_(k) is the harmonicnumber for ion "k". The values of H_(j) and H_(k) may be any non-zeropositive odd integer including 1.

To determine whether two preselected ions can be simultaneouslyregulated in accordance with the present invention, the followingequation: ##EQU5## is utilized where the value of H₂ is any non-zeropositive odd integer. In a preferred embodiment, H₂ is a positive oddinteger from three to nineteen. Thus, a set of values for H₁ aredefined.

The following table illustrates this method for several importantbiological ions:

    __________________________________________________________________________    ION N   AT. WT.                                                                            Fc/Bo                                                                              3    5    7    9    11   13   15   17   19                  __________________________________________________________________________    Cu  1   63.54                                                                              24.147                                                                              72.44                                                                             120.74                                                                             169.03                                                                             217.33                                                                             265.62                                                                             313.92                                                                             362.21                                                                             410.51                                                                             458.80              Ag  2   107.87                                                                             28.448                                                                              85.34                                                                             142.24                                                                             199.13                                                                             256.03                                                                             312.93                                                                             369.82                                                                             426.72                                                                             483.61                                                                             540.51              Gd  3   157.25                                                                             29.272                                                                              87.82                                                                             146.36                                                                             204.90                                                                             263.45                                                                             321.99                                                                             380.53                                                                             439.08                                                                             497.62                                                                             556.16              K   1   39.102                                                                             39.239                                                                             117.72                                                                             196.20                                                                             274.57                                                                             353.15                                                                             431.63                                                                             510.11                                                                             588.59                                                                             667.07                                                                             745.54              Cl  -1  35.453                                                                             43.278                                                                             129.83                                                                             216.39                                                                             302.35                                                                             389.50                                                                             476.06                                                                             562.61                                                                             649.17                                                                             735.72                                                                             822.28              Zn  2   65.37                                                                              46.943                                                                             140.83                                                                             234.71                                                                             328.60                                                                             422.49                                                                             516.37                                                                             610.26                                                                             704.14                                                                             798.03                                                                             891.92              Co  2   58.93                                                                              52.073                                                                             156.22                                                                             260.36                                                                             364.51                                                                             468.66                                                                             572.80                                                                             676.95                                                                             781.09                                                                             885.24                                                                             989.39              Fe  2   55.847                                                                             54.948                                                                             164.04                                                                             274.74                                                                             384.63                                                                             494.53                                                                             604.42                                                                             714.32                                                                             824.21                                                                             934.11                                                                             1044.00             Mn  2   54.94                                                                              55.855                                                                             167.56                                                                             279.27                                                                             390.98                                                                             502.69                                                                             614.40                                                                             726.11                                                                             837.82                                                                             949.53                                                                             1061.24             Na  1   22.99                                                                              66.739                                                                             200.22                                                                             333.70                                                                             467.17                                                                             600.65                                                                             734.13                                                                             867.61                                                                             1001.09                                                                            1134.56                                                                            1268.04             Ca  2   40.08                                                                              76.563                                                                             229.69                                                                             382.82                                                                             535.94                                                                             689.07                                                                             842.20                                                                             995.32                                                                             1148.45                                                                            1301.58                                                                            1454.70             Mg  2   24.32                                                                              126.178                                                                            378.54                                                                             630.89                                                                             803.25                                                                             1135.61                                                                            1387.96                                                                            1640.32                                                                            1892.68                                                                            2145.03                                                                            2397.39             Li  1   6.94 221.085                                                                            663.26                                                                             1105.43                                                                            1547.60                                                                            1989.77                                                                            2431.94                                                                            2874.11                                                                            3316.28                                                                            3758.45                                                                            4200.62             __________________________________________________________________________                                                              8               

If two H₂ values exist which are positive odd integers or which havevalues close to that of positive odd integers, then a harmonic overlapexists at these values. To correspond with the aforementioned overlaprange or band of frequencies which produce simultaneous ion movement ofthe two ionic species (i.e. preferably less than 5% deviation betweenthe actual frequency (f_(cs)) and the f_(ch) values), H₁ should notdeviate more than 2.5% from an odd integer. To better illustrate thismethod, the technique will now be described with reference to Ag⁺⁺ andNa⁺ at a B₀ of 0.2 Gauss.

Ion j=Ag⁺⁺

(f_(c) /B₀)_(j) =28.448

Ion K=Na⁺⁺

(f_(c) /B₀)_(k) =66.739

Therefore, H₁ =0.42625 H₂.

At H₂ values of 3, 5, 7, 9, 11, 13, 15, 17 and 19.

                  TABLE                                                           ______________________________________                                                H.sub.1       H.sub.2                                                 ______________________________________                                                0.42625       (1)                                                             1.279         (3)                                                             2.131         (5)                                                             2.983         (7)                                                             3.84          (9)                                                             4.69          (11)                                                            5.54          (13)                                                            6.39          (15)                                                            7.24          (17)                                                            8.093         (19)                                                    ______________________________________                                    

Based on these calculations, it is apparent that the value of H₁ whereH₂ is 7 (i.e. 2.983), provides the necessary harmonic overlapconditions. Thus,

(f_(c) /B₀)Ag⁺⁺ for the 7th harmonic (H₂ =7) is 199.13

(f_(c) /B₀)Na⁺ for the 3rd harmonic (H₂ =3) is 200.22

Since B₀ =0.2 Gauss=20μ Tesla,

7th f_(c) Ag⁺⁺ =39.826 Hz

3rd f_(c) Na⁺ =40.04 Hz

(This gives Δf=0.214 Hz)

It is important to also note that the overlap can be expanded byincreasing the value of B₀. In the previous example, at 1000μ Tesla,

7th f_(c) Ag⁺⁺ =1991.13 Hz

3rd f_(c) Na⁺ =2002.2 Hz

(This gives Δf=11.07 Hz)

Using this method for determining harmonic overlap for Zn⁺⁺ and Ca⁺⁺ :

    ______________________________________                                        H.sub.1 = .61313 H.sub.2                                                              H.sub.1       H.sub.2                                                 ______________________________________                                                 0.61313      (1)                                                              1.839        (3)                                                              3.066        (5)                                                              4.29         (7)                                                              5.52         (9)                                                              6.74         (11)                                                             7.97         (13)                                                             9.197        (15)                                                            10.42         (17)                                                            11.65         (19)                                                    ______________________________________                                    

It can be seen that the 5 th harmonic of Zn⁺⁺ overlaps with the 3rdharmonic of Ca++.

In its most preferred embodiment, fluctuations in the local fieldcomponent which would otherwise alter the predetermined relationshipprovided by multiple ion tuning are counter-balanced by a microprocessorin association with the magnetic field generating means. Briefly,changes in the composite field due to changes in the local component arepreferably measured by magnetic field sensor in association with themagnetic field generator. The microprocessor then adjusts the frequencyof the field and/or the field strength to maintain the desired ratio offrequency-to-average magnetic flux density, which is always a non-zeroaverage value. This technique is also suitable for counter-balancingchanges in the local component in that embodiment of the presentinvention in which a single ionic species is regulated using a higherodd harmonic frequency. The microprocessor may also be programmed toautomatically calculate f_(cs) based on an input of the q/m ratios ofthe ions to be regulated.

The present invention is particularly useful in controlling tissuegrowth using the apparatus shown in FIG. 8 of the drawings for effectingmultiple ion tuning and in the treatment and prevention of osteoporosisin this manner and as shown in FIG. 9 of the drawings. Morespecifically, with respect to FIG. 8 of the drawings, treatmentapparatus 30 is shown having treatment heads 32 and 34. Each treatmenthead contains a field coil such that treatment heads 32 and 34 comprisea pair of Helmholtz coils. To bring about a therapeutic treatment of abone condition such as a fracture, non-union or delayed union, treatmentheads 32 and 34 are positioned so that a uniform magnetic field can begenerated in space 36, illustrated here as being occupied by fracturedends 40 and 42 of human femur 38. In order to accelerate the rate atwhich union of the fractured ends occurs, in this embodiment of thepresent invention, the frequency of the composite magnetic field ismaintained at about 76 Hertz which is very close (within 5 percent) tothe cyclotron resonance frequency of Ca⁺⁺ multiplied by a factor of 5and Mg⁺⁺ multiplied by a factor of 3, where the non-zero net averagevalue is 20 microTesla (peak-to-peak amplitude 40μ Tesla). Changes inthe local component which would otherwise change this relationship arecounter-balanced by a magnetic field sensor (not shown) and amicroprocessor (not shown) which sense changes in the local componentand adjusts the field and/or applied magnetic flux to maintain thisprecise relationship. Treatment is continued until such time thatbeneficial results are attained, for example, from about one-half hourto six hours per day for approximately twelve weeks. Treatment withinthese parameters is effective in stimulating the growth of cartilaginoustissue, non-osseous non-cartilaginous tissue and solid connectivetissue, as well as the local treatment or prevention of osteoporosis andthe systemic treatment or prevention of osteoporosis utilizing theapparatus shown in FIG. 9.

The following examples are provided to more fully illustrate the presentinvention and are not intended to limit the scope of the invention asdefined in the appended claims

EXAMPLE 1

Diatoms were exposed to a fluctuating magnetic field in accordance withthe present invention at both the fundamental frequency of 16 Hertz forCa⁺⁺ and then at odd multiples as provided by the equation f_(ch)=XBq/2πm for Ca⁺⁺. It was noted than in addition to the fundamentalfrequency, where X was 3, 5 and 15, movement of diatoms (which is knownto be brought about by increase in the intracellular concentration ofcalcium ions) was notably increased. Where X was 7, 9, 11, 13, and 17,increased motility was not produced.

EXAMPLE 2

Isolated in vitro 8-day chick femurs were exposed to a magnetic fieldharmonically "tuned" simultaneously for calcium and magnesium ions,according to the equation f_(ch) =XBq/2πm, where X=5 for Ca⁺⁺ and X=3for Mg⁺⁺. At a non-zero net average value of B at 20.9 microTesla, whichwas the composite field as previously explained, f_(cs) was set at 80Hz. Increased bone growth was observed over controls.

In more detail, freshly-laid fertile white leghorn chicken eggs wereobtained and which were incubated in a 100% humidified atmosphere at 40°C. for 8 days, and then removed and candled. For each run of theexperiments, 26 eggs with normal-appearing embryos were selected. Theeggs were opened, and the embryos removed to a sterile Petri dish. Anyembryos abnormal in development or staging were discarded. The femurs ofthe embryos' legs were removed by blunt dissection with forceps andtransferred in right-left pairs to sterile gauze squares moistened withHanks' Balanced Salt Solution (HBSS) in another sterile dish. From thisdish, pairs were removed to squares of dry, sterile unbleached muslin,where they were rolled back and forth under a dissecting microscopeuntil adhering tissue was removed, leaving bones stripped of all tissueexcept the perichondrium/periosteum. Tissue removal was confirmedmicroscopically. The right leg of each pair was reserved as a control,the left thus became an experimental subject.

The isolated femurs prepared for culture by the above method were placedinto the wells of 12-well culture plates (Linbro). A small triangulartype 316 stainless steel mesh screen was placed in each well. Thecorners had been folded under to lift the mesh slightly away from thebottom of the plate and allow for media circulation. A sterile triangleof thoroughly washed ordinary lens paper was placed atop the meshscreen, and the femurs were oriented in orthogonally positioned pairs onthe lens paper. Thus, each femur could be identified later, since thewells were also numbered sequentially.

As each well was completed, it was given a 0.5 mil aliquot of sterileBGJ_(b) medium (Fitton-Jackson modification, GIBCO) containingantibiotics and antimycotics (GIBCO). This amount was just sufficient tosaturate the lens tissue and produce a meniscus of medium over theexplanted femurs. It was noted that too much medium produced impairedgrowth, since gas exchange was also impaired if the femurs were beneaththe surface of the medium. As soon as each plate was completed, it wascovered and placed in either a control or experimental position within awater-jacketed CO₂ incubator containing a 100% humidified atmosphere of5 percent CO₂ in air at 40° C. Subsequent culture consisted of sevendays in the incubator, with fresh medium ever other day.

The dishes containing the left femurs were placed between 15 cm diameterHelmholtz-aiding coils according to the method of the present invention.The non-zero average value of the B field strength was set at 20.9microTesla. A Beckman FG-2 function generator supplied an 80 Hz ac sinewave along the coil axis, whose amplitude was set at 30 microTesla,peak-to-peak. The frequency of the signal was checked with a BeckmanUC-10 frequency counter calibrated against an NBS-referrable source. Theamplitude of the ac and static magnetic fields was checked with asingle-axis fluxgate magnetometer (Schonstedt Instruments Model 2200-DS)calibrated against NBS standard. AC ampliltude was read by feeding theanalogue output from the magnetometer to a Tektronix 204A oscilloscopewhich had also been calibrated against NBS-referrable voltage standards.The magnetic fields were passed through the femurs horizontally.

For the simultaneous treatment, with B set at 20.9 microTesla and the acfrequency (f_(cs)) set at 80 Hz, calculation will readily verify thatthese conditions represent a frequency within 5 percent of the f_(ch)values for CA⁺⁺ where X is 5 and Mg⁺⁺ where X is 3. Independently, thesef_(ch) values had been shown previously to be effective for stimulatingdiatom movement. By using this combination, a concurrent stimulation forboth ions could be achieved.

The control cultures were maintained in the same chamber as theexperimentals, but shielded from the magnetic fields. The ac magneticfield strength to which the control femurs were subjected was at leasttwo orders of magnitude less than the experimentals (not greater than0.3 microTesla, peak-to-peak). The ambient 60 Hz magnetic field in thechambers was less than 0.1 microTesla.

At the end of the experiment, the medium was removed from each well ofthe dishes, and was replaced with an equal amount of Millonig's NeutralBuffered Formalin. After 24 hours to allow for fixation and shrinkage,the femurs were removed gently from the lens paper and the length andcentral diaphyseal diameters were measured with a pair of metric verniercalipers. The measurements were made and recorded in a blind manner. Thefemurs were then returned to the wells, but were separated by a smallpaper divider to keep them separate and identifiable. They were thendecalcified and embedded through alcohols and benzene into 54°Paraplast, then cut longitudinally at 8 microns and stained with Mayer'sHaematoxylin and Eosin.

The sections were examined under a light microscope (Olympus CH-2) andmeasurements of the diaphyseal collar length and thickness were madewith an ocular micrometer. An assessment of the degree of maturation wasalso made, together with notes on the histological appearance of thebones. Detailed morphometric analysis was not undertaken, since thedifferences were either so striking that a resort to statistics wasdeemed unnecessary, except with regard to the measurements of length,diameter, collar length, and collar thickness. For those measurements, aStudent's T-test of the paired experimentals and controls was performed.The experiment was performed in duplicate, so that there were 96 bonesin the ionic group, 48 experimentals and 48 controls. These numbers gaveclear statistic inferences.

The numerical results of all experiments are presented in Table I below:

                  TABLE I                                                         ______________________________________                                        Results of Chick Femur Tests                                                  Category of Measurement                                                                           Ca/Mg                                                     ______________________________________                                        1.      Bone Length (mm)                                                                              8.7*                                                          S.D.            0.8                                                           Controls        7.8                                                           S.D.            0.7                                                   2.      Bone Diameter (mm)                                                                            1.03*                                                         S.D.            0.12                                                          Controls        0.70                                                          S.D.            0.08                                                  3.      Length/Diameter 9.1*                                                          S.D.            0.7                                                           Controls        11.1                                                          S.D.            1.03                                                  4.      Collar Length (mm)                                                                            2.31*                                                         S.D.            0.53                                                          Controls        1.16                                                          S.D.            0.23                                                  5.      Collar Thickness (mm)                                                                         0.045*                                                        S.D.            0.014                                                         Controls        0.025                                                         S.D.            0.008                                                 ______________________________________                                         *p < .01 compared to paired control value                                

Controls

There was no statistically significant difference between the values forthe two runs. Hence, they were pooled.

The histological appearance of the controls did not vary from run torun. The picture they presented was essentially normal. The ends of thebones were composed of relatively condensed and cellular hyalinecartilage. The diaphyseal collar was quite thin, but well-ossified,while the central diaphyseal region had modestly hypertrophiedchondrocytes, with a few pyknotic nuclei, but little or no calcificationof the cartilage matrix.

Experimental Treatment

When both calcium and magnesium ions were subjected to CR conditions,the results were essentially a combination of those seen previously forcalcium and magnesiium separately. The bones were significantly (p<0.01)lengthened (+12%) and thickened (+47%), and the diaphyseal collar length(+99%) and thickness (+80%) were also increased (p<0.01). Robustnessincreased by 22%.

Histologically, the bones were, as with calcium ion stimulation,advanced with respect to calcification, the central diaphyseal regionshowing marked calcification. However, the degree of this effect wasslightly less than with calcium stimulation alone. The rest of the boneshowed generalized enlargement, as with magnesium ion tuning alone.

EXAMPLE 3

A study of simultaneous multiple ion tuning was performed using fibularostectomies in skeletally mature rabbits. Twelve skeletally mature (2.5Kg) New Zealand White rabbits of mixed sex were divided into two groupsof six animals each and anaesthetized. After anaesthesia, both legs wereshaved laterally and painted with betadyne solution. An incision wasmade 1 cm caudal to the knee, extending for 2.5 cm. The muscles of theanterior and peroneal compartments were separated to expose the fibula.The periosteum was split and reflected from the bone. On the right, theperiosteum was allowed to return to place. These bones served as thesham operations. On the left, a 1 cm piece of the fibula was removedfrom the bone, beginning approximately 1 cm cranial to the union offibula and tibia. The periosteum was allowed to return. These bonesserved as the operated series. The wounds of both sides were then closedin layers, ending with stainless steel sutures. The animals were thenreturned to their cages for recovery.

Six animals were placed in cages which lay between pairs ofHelmholtz-aiding coils., according to the method of the presentinvention. They were stimulated for 1/2 hour per day. The six animalsthen exposed to a fluctuating magnetic field tuned to calcium andmagnesium simultaneously, using the method of the present invention. Thenon-zero average value of the (B) field was 40μ Tesla, 30 microTeslapeak-to-peak, and the frequency (f_(cs)) was 153 Hz. This set ofconditions, as may be readily seen, provides a value f_(cs) which iswithin 5 percent of f_(ch) for calcium where X is 5 and for magnesiumwhere X is 3. The other six animals received no magnetic fieldstimulation and served as controls.

After one month of stimulation, the rabbits were removed from the cagesand necrotized by CO₂ inhalation. The legs were disarticulated andremoved. A-P radiographs were taken of each leg, and the muscle tissuewas then stripped from the bones. The diameters of fabellae and calluswere measured from the radiographs with a digital micrometer. Thefibulas were removed and clamped into a cantilever bending testing jig.Each femur was then bent in the A-P axis by moving the bone with amicrometer screw against the tip of a force transducer positioned 1.5 cmabove the tip of the clamp jaws. This length of bone included theostectomy site. The bones were bent 1 mm, and the force required toproduce the bending was recorded by an oscillograph connected to acomputer, which produced on-screen graphs of force vs. deflection. TheF-D ratios of operated vs. sham-operated sided were compared.

The results of the tests are presented graphically in Table A.

                  TABLE A                                                         ______________________________________                                        OSTECTOMY RESULTS                                                                      Fabellar Diam.                                                                             Callus Diam.                                            Condition                                                                              (mm)         (mm)        F-D Ratio                                   ______________________________________                                        Control  2.73 ± .39                                                                              2.81 ± .52                                                                              .57 ± .26                               Ca/Mg 5/3                                                                              3.77 ± .49#                                                                             3.99 ± .84#                                                                            1.88 ± .74#                              ______________________________________                                    

From these results, it can be seen that the application of fieldsharmonically tuned to cyclotron resonance conditions for calcium andmagnesium simultaneously, according to the method of the presentinvention, produces the growth and osteogenetic effects of magnesiumwith the mineralization effects of calcium.

These examples offer evidence as to the efficacy of both odd multipleharmonic tuning and the utility of simultaneous turning to more than oneion. It is to be understood that other simultaneous tunings arepossible, using harmonic degeneracies, and that the present examples arenot meant to be exclusive of other applications or pairings. Any pairingwhere a degeneracy can be found at complementary odd harmonics iscontemplated by the present invention.

What is claimed is:
 1. An apparatus for regulating the movement of apreselected ion across a cell membrane, comprising:means for generatingan applied magnetic field parallel to a predetermined axis projectingthrough a space in which at least one living cell is positioned in thepresence of a preselected ion, said applied magnetic field resulting ina magnetic flux density in said space of a known average value parallelto said predetermined axis; means associated with said magnetic fieldgenerating means for fluctuating said magnetic flux density such thatsaid known average value is a non-zero average value; means for creatinga predetermined relationship between the frequency of said fluctuationsand said non-zero average value of said magnetic flux density, whereinsaid predetermined relationship is determined using the equation f_(ch)=XBq/2πm, where f_(ch) is the frequency of the fluctuating magnetic fluxdensity parallel to said predetermined axis in Tesla, q is the charge ofsaid preselected ion in Coulombs, m is the mass of said preselected ionin kilograms, and X is a selected odd integer greater than
 1. 2. Theapparatus recited in claim 1, wherein said space is subject to a localmagnetic field having a component vector parallel to said predeterminedaxis and wherein said non-zero average value of said magnetic fluxdensity is a net average value which includes the magnetic flux densityof said component vector of said local magnetic field.
 3. The apparatusrecited in claim 1, wherein said selected odd integer is selected fromthe group consisting of odd integers from 1 to
 19. 4. The apparatusrecited in claim 1, wherein said means for creating said predeterminedrelationship includes a magnetic field sensor and a microprocessor.
 5. Amethod for regulating the movement of a preselected ion across a cellmembrane, comprising:generating an applied magnetic field parallel to apredetermined axis projecting through a space in which at least oneliving cell is positioned in the presence of a preselected ion, saidapplied magnetic field resulting in a magnetic flux density in saidspace of a known average value parallel to said predetermined axis;fluctuating said magnetic flux density such that said known averagevalue is a non-zero average value; creating a predetermined relationshipbetween the frequency of said fluctuations and said non-zero averagevalue of said magnetic flux density, wherein said predeterminedrelationship is determined using the equation f_(ch) =XBq/2πm, wheref_(ch) is the frequency of the fluctuating magnetic flux density inHertz, B is the non-zero average value of the flux density parallel tosaid predetermined axis in Tesla, q is the charge of said preselectedion in Coulombs, m is the mass of said preselected ion in kilograms, andX is a selected odd integer greater than
 1. 6. The method recited inclaim 5, wherein said space is subject to a local magnetic field havinga component parallel to said predetermined axis and wherein saidnon-zero average value of said magnetic flux density is a net averagevalue which includes the magnetic flux density of said component of saidlocal magnetic field.
 7. The method recited in claim 5, wherein saidselected odd integer is selected from the group consisting of oddintegers from 1 to
 19. 8. The method recited in claim 5, wherein said atleast one living cell is a region of living tissue of a biologicalsubject.
 9. The method recited in claim 8, wherein said region of livingtissue is bone tissue and said biological subject is a human or animalsubject.
 10. The method recited in claim 9, wherein said predeterminedrelationship stimulates growth of said bone tissue.
 11. The methodrecited in claim 9, wherein said bone tissue is afflicted withosteoporosis and wherein said method therapeutically treats said bonetissue by reducing the extent of said osteoporosis.
 12. The methodrecited in claim 9, wherein said method prevents osteoporosis.
 13. Themethod recited in claim 5, wherein said at least one living cell issubstantially an entire human or animal subject afflicted withosteoporosis and wherein said method systemically therapeutically treatssaid subject by reducing the extent of said osteoporosis.
 14. The methodrecited in claim 5, wherein said at least one living cell issubstantially an entire human or animal subject and wherein said methodprevents osteoporosis.
 15. The method recited in claim 8, wherein saidliving tissue is non-osseous, non-cartilaginous connective tissue, saidbiological subject is human or animal, and said method stimulates thegrowth of said non-osseous, non-cartilaginous connective tissue.
 16. Themethod recited in claim 8, wherein said living tissue is cartilaginoustissue, said biological subject is human or animal, and said methodstimulates the growth of said cartilaginous tissue.
 17. An apparatus forsimultaneously regulating the movement of at least two different ionsacross a cell membrane, comprising:means for generating an appliedmagnetic field parallel to a predetermined axis projecting through aspace in which at least one living cell is positioned in the presence ofat least two different preselected ions, said applied magnetic fieldresulting in a magnetic flux density in said space of a known averagevalue parallel to said predetermined axis; means associated with saidmagnetic field generating means for fluctuating said magnetic fluxdensity such that said know average value is a non-zero average value;means for determining a value f_(ch) for each of said preselected ions,where f_(ch) =XBq/2πm, B is said non-zero average value of said magneticflux density along said axis, q is the charge of said ion in Coulombs, mis the mass of said ion in kilograms, and X is a selected positivenon-zero odd integer; means for selecting a value f_(cs) in Hertz fromwhich each value f_(ch) deviates less than a predetermined percentage;fluctuating said magnetic field parallel to said axis at a rate which isequal to said f_(cs) value; and maintaining the ratio of said f_(cs)rate of fluctuation to said non-zero average value of said magnetic fluxdensity parallel to said axis.
 18. The apparatus recited in claim 17,wherein said space is subject to a local magnetic field having acomponent parallel to said predetermined axis and wherein said non-zeroaverage value of said magnetic flux density is a net average value whichincludes the magnetic flux density of said component of said localmagnetic field.
 19. The apparatus recited in claim 17, wherein saidselected odd integer is selected from the group consisting of 1, 3, 5,7, 9, 11, 13, 15, 17, and
 19. 20. The apparatus recited in claim 17,wherein said apparatus includes a magnetic field sensor and amicroprocessor.
 21. A method for simultaneously regulating the movementof at least two different ions across a cell membrane, comprising thesteps of:generating a fluctuating applied magnetic field parallel to apredetermined axis projecting through a space in which at least oneliving cell is positioned in the presence of at least two differentpreselected ions, said applied magnetic field resulting in a magneticflux density in said space of a known non-zero average value parallel tosaid predetermined axis; fluctuating said magnetic flux density suchthat said known average value is a non-zero average value; determining avalue f_(ch) for each of said preselected ions where f_(ch) =XBq/2πm,where B is said non-zero average value of said magnetic flux densityalong said axis, q is the charge of said ion in Coulombs, m is the massof said ion in kilograms and X is a selected positive non-zero oddinteger; selecting a value f_(cs) in Hertz from which each value f_(ch)deviates less than a predetermined percentage; fluctuating said magneticfield parallel to said axis at a rate which is equal to said f_(cs)value; and maintaining the ratio of said f_(cs) rate of fluctuation tosaid non-zero average value of said magnetic flux density parallel tosaid axis.
 22. The method recited in claim 21, wherein saidpredetermined percentage is less than 5 percent.
 23. The inventionrecited in claim 21, wherein said at least two different preselectedions comprises three ions.
 24. The method recited in claim 21, whereinsaid selected odd integer is selected form the group consisting of 1, 3,5, 7, 9, 11, 13, 15, 17 and
 19. 25. The method recited in claim 21,wherein said at least one living cell is a region of living tissue of abiological subject.
 26. The method recited in claim 25, wherein saidregion of living tissue is bone tissue, said biological subject is ahuman or animal subject, said at least 2 preselected ions are Ca⁺⁺ andMg⁺⁺, said value of X is 5 for said f_(ch) value of Ca⁺⁺ and said valueof X is 3 for said f_(ch) value of Mg⁺⁺.
 27. The method recited in claim26, wherein said value of f_(cs) is about 75 Hertz and said methodstimulates growth of said bone tissue.
 28. The method recited in claim26, wherein said bone tissue is afflicted with osteoporosis and whereinsaid method therapeutically treats said bone tissue by reducing theextent of said osteoporosis.
 29. The method recited in claim 26, whereinsaid method prevents osteoporosis.
 30. The method recited in claim 21,wherein said at least one living cell is substantially an entire humanor animal subject afflicted with osteoporosis and wherein said methodsystemically therapeutically treats said subject by reducing saidosteoporosis.
 31. The method recited in claim 21, wherein said at leastone living cell is substantially an entire human or normal subject andwherein said method prevents osteoporosis.
 32. The method recited inclaim 25, wherein said living tissue is non-osseous, non-cartilaginousconnective tissue, said biological subject is human or animal, and saidmethod stimulates the growth of said non-osseous, non-cartilaginousconnective tissue.
 33. The method recited in claim 25, wherein saidliving tissue is cartilaginous tissue, said biological subject is humanor animal, and said method stimulates the growth of said cartilaginoustissue.
 34. A method of regulating transmembrane ion movement ofpreselected ionic species comprising of steps of exposing at least oneliving cell to a fluctuating magnetic flux density in the presence ofsaid ionic species and controlling the rate of said fluctuations suchthat f_(c) =Bq/2πm, where f_(c) is the frequency of the fluctuatingmagnetic flux density in hertz, B is a non-zero average value of theflux density in Tesla, q is the charge of said preselected ionic speciesin Coulombs and m is the mass of said preselected ionic species inkilograms.
 35. The method recited in claim 34, wherein said magneticflux density is fluctuated at a value determined by multiplying f_(c) byan odd integer.
 36. A method of simultaneously regulating thetransmembrane movement of at least two preselected ions in a biologicalsystem, said method comprising the steps of identifying thecharge-to-mass ratios of said at least two preselected ions, determininga value f_(cs) for said at least two preselected ions, said f_(cs) valuebeing based on the cyclotron resonance frequencies of said at least twopreselected ions using said charge-to-mass ratios, exposing a biologicalsystem which includes said at least two preselected ions and abiological membrane to a fluctuating magnetic field having a non-zeroaverage flux density and a fluctuating magnetic field at a frequencysubstantially equal to said fcs value, thereby causing transmembranemovement of said at least two preselected ions across said biologicalmembrane.